Volume 54, Number 4, July-August 2020
|Page(s)||949 - 959|
|Published online||16 April 2020|
New second-order radial epiderivatives and applications to optimality conditions★
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074 PR China
Accepted: 14 March 2019
In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.
Mathematics Subject Classification: 90C26 / 90C46
Key words: Set-valued optimization problems / second-order weakly composed radial epiderivatives / Benson proper efficient solutions / second-order optimality conditions
This research was partially supported by the Natural Science Foundation Project of CQ CSTC (Nos.cstc2015jcyjA30009, cstc2015jcyjBX0131, cstc2017jcyjAX0382), the Program of Chongqing Innovation Team Project in University (no.CXTDX201601022), the National Natural Science Foundation of China (No.11571055) and Chongqing Jiaotong University Graduate Education Innovation Foundation Project (No.2018S0152).
© EDP Sciences, ROADEF, SMAI 2020
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